Question: Simplify the following expression: $k = \dfrac{r^2 + 13r + 42}{r + 6} $
First factor the polynomial in the numerator. $ r^2 + 13r + 42 = (r + 6)(r + 7) $ So we can rewrite the expression as: $k = \dfrac{(r + 6)(r + 7)}{r + 6} $ We can divide the numerator and denominator by $(r + 6)$ on condition that $r \neq -6$ Therefore $k = r + 7; r \neq -6$